Author

# Przemyslawa Kanarek

Bio: Przemyslawa Kanarek is an academic researcher. The author has contributed to research in topics: Permutation & Random permutation. The author has an hindex of 2, co-authored 2 publications receiving 37 citations.

##### Papers

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TL;DR: The main result of the paper is an algorithm for generating random permutations that runs in O(log log n) time and uses O(n1+o(1)) processors on the CREW PRAM, which is the first o(log n) -time CREWPRAM algorithm for this problem.

Abstract: We consider the problem of generating random permutations with uniform distribution. That is, we require that for an arbitrary permutation π of n elements, with probability 1/n! the machine halts with the i th output cell containing π(i) , for 1 ≤ i ≤ n . We study this problem on two models of parallel computations: the CREW PRAM and the EREW PRAM. The main result of the paper is an algorithm for generating random permutations that runs in O(log log n) time and uses O(n
1+o(1)
) processors on the CREW PRAM. This is the first o(log n) -time CREW PRAM algorithm for this problem. On the EREW PRAM we present a simple algorithm that generates a random permutation in time O(log n) using n processors and O(n) space. This algorithm outperforms each of the previously known algorithms for the exclusive write PRAMs. The common and novel feature of both our algorithms is first to design a suitable random switching network generating a permutation and then to simulate this network on the PRAM model in a fast way.

25 citations

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25 Sep 1996TL;DR: This work considers the classical problem of generating random permutations with the uniform distribution, and studies the problem on two models of parallel computations: the CREW PRAM and the EREWPRAM.

Abstract: We consider the classical problem of generating random permutations with the uniform distribution. That is, we require that for an arbitrary permutation π of n elements, with probability 1/n! the machine halts with the ith output cell containing π(i), for 1≤i≤n. We study this problem on two models of parallel computations: the CREW PRAM and the EREW PRAM.

12 citations

##### Cited by

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19 Aug 2009TL;DR: The results, which employ Markov-chain techniques, enable the construction of a practical and provably-secure blockcipher-based scheme for deterministically enciphering credit card numbers and the like using a conventional blockCipher.

Abstract: We analyze the security of the Thorp shuffle, or, equivalently, a maximally unbalanced Feistel network. Roughly said, the Thorp shuffle on N cards mixes any N 1 ? 1/r of them in $O(r\lg N)$ steps. Correspondingly, making O(r) passes of maximally unbalanced Feistel over an n-bit string ensures CCA-security to 2 n(1 ? 1/r) queries. Our results, which employ Markov-chain techniques, enable the construction of a practical and provably-secure blockcipher-based scheme for deterministically enciphering credit card numbers and the like using a conventional blockcipher.

117 citations

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TL;DR: The algorithm can be directly translated into an optimal external memory algorithm if fast memory for √ nB (1 + o (1) + O ( B ) elements is available where B is the page size.

Abstract: A simple randomized algorithm for generating a uniformly distributed random permutation of size n is investigated. It works in time O ( n P + T comm ( n P , P) + T prefix (P)) on P processors with high probability, where T comm ( k , P ) is the time for randomly sending or receiving k elements on each processor and T prefix ( P ) is the time for computing a prefix sum. The algorithm can be directly translated into an optimal external memory algorithm if fast memory for √ nB (1 + o (1)) + O ( B ) elements is available where B is the page size. Due to its simplicity, the same algorithm even outperforms the straightforward method on mainstream workstations if the cache is taken to be the fast memory and the main memory is treated like external memory. The algorithm is almost four times faster on a MIPS R10000 machine.

52 citations

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18 Aug 2013TL;DR: A new shuffling algorithm, called Mix-and-Cut, is provided that provides a provably-secure block cipher even for adversaries that can observe the encryption of all N = 2 n domain points.

Abstract: We provide a new shuffling algorithm, called Mix-and-Cut, that provides a provably-secure block cipher even for adversaries that can observe the encryption of all N = 2 n domain points. Such fully secure ciphers are useful for format-preserving encryption, where small domains (e.g., n = 30) are common and databases may well include examples of almost all ciphertexts. Mix-and-Cut derives from a general framework for building fully secure pseudorandom permutations (PRPs) from fully secure pseudorandom separators (PRSs). The latter is a new primitive that we treat for the first time. Our framework was inspired by, and uses ideas from, a particular cipher due to Granboulin and Pornin. To achieve full security for Mix-and-Cut using this framework, we give a simple proof that a PRP secure for (1 − e)N queries (recently achieved efficiently by Hoang, Morris, and Rogaway’s Swap-or-Not cipher) yields a PRS secure for N queries.

49 citations

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01 Jan 1999TL;DR: These are the first non-trivial applications of non-Markovian coupling for proving rapid m&g of Markov chains in distributed and parallel systems and all the protocols are simple, elegant and epling.

Abstract: We analyze various stochastic processes for generating permutations almost uniformlv at random in distributed and parallel systems. All our protocols are simple, elegant and epling, and for the third one we prove the existence of a non-Markovian coupling. To the best of our knowledge, these are the first non-trivial applications of non-Markovian coupling for proving rapid m&g of Markov chains. We annlv our analvsis in diverse areas. We develon a simple permutation network of a polylogarithmic depth generating permutations with almost uniform distribution. A simple EREW PRAM algorithm generating random permutations in time O(log log n) with O(nlog’(r) n) processors follows. We improve technique of cryptographic defense against traffic analysis by showing that the underlying stochastic urocess converees in time Oflonnl finstead of ~olvlogarith-mic time) and

46 citations

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26 Mar 2007TL;DR: This work presents an algorithm for selecting such a random permutation of n elements and evaluating efficiently the permutation and its inverse over arbitrary inputs using an underlying deterministic RNG (random number generator).

Abstract: Existing symmetric encryption algorithms target messages consisting of elementary binary blocks of at least 64 bits. Some applications need a block cipher which operates over smaller and possibly nonbinary blocks, which can be viewed as a pseudo-random permutation of n elements. We present an algorithm for selecting such a random permutation of n elements and evaluating efficiently the permutation and its inverse over arbitrary inputs. We use an underlying deterministic RNG (random number generator). Each evaluation of the permutation uses O(log n) space and O((log n)3) RNG invocations. The selection process is "perfect": the permutation is uniformly selected among the n! possibilities.

40 citations